He said NATO is “working hard” to resolve the “legitimate” issues raised by Turkey.
Mr Stoltenberg had previously insisted that both countries would be welcomed “with open arms”, but Turkey blocked their applications.
Ankara accuses them of offering refuge to the Kurdistan Workers’ Party (PKK), a group classified as “terrorist” by Turkey and its Western allies.
“I would like this matter to be resolved as soon as possible,” Stoltenberg said Sunday at a joint press conference in Finland with Finnish President Sauli Niinisto.
However, “the Madrid summit was never a deadline,” he said.
At the beginning of June, during a visit to Washington, Mr. Stoltenberg had declared that his “intention” was to settle the question before the meeting which is due to open on June 28.
Mr Stoltenberg said Ankara had raised “legitimate concerns”.
“We must understand and remember that no other NATO ally has suffered more terrorist attacks than Turkey. And also that Turkey is an important ally with a strategic geographical location,” he stressed.
Any NATO membership agreement must be approved unanimously by its thirty members.
The two Nordic countries have repeatedly expressed surprise at Turkey’s objections, saying Ankara had signaled its support for their membership applications until they submitted them.